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Elizabeth is a Senior Academic Specialist in the Program in Mathematics Education at Michigan State University, USA, an author of the Connected Mathematics Project, and a Principal Investigator for two National Science Foundation Research grants investigating middle school mathematics learning and engagement with digital resources.
1. What’s your earliest memory of doing mathematics?
At a young age I was more interested in reading than mathematics. This changed in 8th grade when I was introduced to applications in maths. I found that I was quite good at it and enjoyed it! But high school geometry was the big turning point. I loved proving conjectures and studying properties of shape.
2. How has mathematics education changed in the time you have been involved in it?
It hasn’t changed much (at least not as much as I’d like it to). Maths has always focused on direct instruction around a set of isolated skills and less on things like understanding and connecting big ideas. We now know a lot from literature in psychology and maths education that if we can unpack the understandings of big mathematical ideas and embed these understandings in a sequence of contextual based problems, it can aid learning. Contextual open problems are very important as they provide students with a variety of entry points to the problem and an anchor on which to develop and recall their understanding of the embedded mathematical idea.
3. Tell me about a time in your career when something totally flabbergasted you.
I have always said that ‘I’ll quit when I stop learning from my students’. What has become apparent throughout my career is that everyone does things in different ways. I have been surprised by my students’ insights, conjectures, and the connections they make when given the right learning environment. This has happened numerous times and these moments have and will stay with me.
4. Do you practise mathematics differently in company?
I think I work in the same way in company and without company. I tend to look for big ideas and I use estimation a lot to get a sense of the answer. I also appreciate the differences between learners: some need time on their own; some need discourse and collaboration to verbalise their thinking as they work on the solution; others prefer to think privately and then write about their findings. I tend to think out loud and will often contradict or change my mind out loud, whether in company or not!
5. Do you think a brilliant maths teacher is born or made?
Both. The kind of teacher needed to create inquiry-based classrooms where students and teachers are collaboratively engaged in asking questions, making conjectures, validating, connecting their knowledge to prior knowledge, and communicating their findings is different than it was 50 or 60 years ago. Teachers need to have intellectual curiosity about and enthusiasm for mathematics and a deep knowledge of the learner, as well as a warm, supportive connection with each student. Some teachers seem to take naturally to this, but I believe that others can grow into this if given support.
Much of my and my colleagues’ professional activities have been working with mathematics teachers to change the dynamics of the classroom to one where students and teachers are engaged in problem solving; asking ‘what if’ questions, making conjectures, validating, connecting their knowledge to prior knowledge, and communicating their findings. They need to experience problem-solving, deeper mathematics learning and effective pedagogy that goes with it, and strategies to help transfer their knowledge to the classroom. With high-quality professional development and a collaborative community, teachers can grow into these roles.
6. What’s the most fun a mathematician can have?
Seeing students come alive and be inventive. Students are problem-solvers and we need to let them mathematize.
7. Do you have a favourite maths joke?
I don’t have a favourite one, but I often use cartoons when teaching maths.
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